{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian inference\n",
    "The following notebook is a review of the key elements involved in a Bayesian Inference. The attempt is made to let you know the most fundemental means in Pattern Recognition. \n",
    "\n",
    "In order to make it successful, the code works make some examples to help you to show the theme by making abstract into concrete."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Math konwledge\n",
    "\n",
    "*If we use English words to discribe Bayesian formula:*\n",
    "\n",
    "$ posterior = \\frac{likelihood * prior}{evidence} $\n",
    "\n",
    "$ \\color{orange}{Minimum-error-rate classification:} $\n",
    "\n",
    "$If$ $ P(\\omega_1|x) > P(\\omega_2|x) $, $then$ $ x \\in \\omega_1 $;\n",
    "\n",
    "$If$ $ P(\\omega_1|x) < P(\\omega_2|x) $, $then$ $ x \\in \\omega_2 $.\n",
    "\n",
    "Bayesian formula: $ P(\\omega_i|X) = \\frac{P(X|\\omega_i)P(\\omega_i)}{P(X)} $\n",
    "\n",
    "$ \\color{orange}{Minimum risk Bayes decision making:} $\n",
    "\n",
    "$If$ $ R(a_k|x) = \\min\\limits_{i = 1, 2, ……, M}R(a_i|x)$ $,then$ $ x\\in \\omega_k $\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import random\n",
    "import scipy.stats as stats\n",
    "from sklearn import datasets\n",
    "from sklearn import model_selection\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "# 加载数据集\n",
    "def load_dataset():\n",
    "    iris = datasets.load_iris()\n",
    "    return iris\n",
    "# 划分数据集为数据和对应类别\n",
    "def split_dataset(dataset):\n",
    "    X = dataset.data[:, 0: 4].astype(float)\n",
    "    Y = dataset.target\n",
    "    validation_size = 0.20\n",
    "    X_train, X_validation, Y_train, Y_validation = \\\n",
    "            model_selection.train_test_split(X, Y, test_size=validation_size)\n",
    "    return X_train, X_validation, Y_train, Y_validation\n",
    "# 将每一类的每个属性划分出来，便于计算\n",
    "def split_out_attributes(X, Y):\n",
    "    c1_1 = c1_2 = c1_3 = c1_4 = []\n",
    "    c2_1 = c2_2 = c2_3 = c2_4 = []\n",
    "    c3_1 = c3_2 = c3_3 = c3_4 = []\n",
    "    for i in range(len(Y)):\n",
    "        if (Y[i] == 0):\n",
    "            c1_1.append(X[i, 0])\n",
    "            c1_2.append(X[i, 1])\n",
    "            c1_3.append(X[i, 2])\n",
    "            c1_4.append(X[i, 3])\n",
    "        elif (Y[i] == 1):\n",
    "            c2_1.append(X[i, 0])\n",
    "            c2_2.append(X[i, 1])\n",
    "            c2_3.append(X[i, 2])\n",
    "            c2_4.append(X[i, 3])\n",
    "        elif (Y[i] == 2):\n",
    "            c3_1.append(X[i, 0])\n",
    "            c3_2.append(X[i, 1])\n",
    "            c3_3.append(X[i, 2])\n",
    "            c3_4.append(X[i, 3])\n",
    "        else:\n",
    "            pass\n",
    "    return [c1_1, c1_2, c1_3, c1_4,\n",
    "            c2_1, c2_2, c2_3, c2_4,\n",
    "            c3_1, c3_2, c3_3, c3_4]\n",
    "# 计算每一类的期望\n",
    "def cal_mean(attributes):\n",
    "    c1_1, c1_2, c1_3, c1_4, c2_1, c2_2, c2_3, c2_4, c3_1, c3_2, c3_3, c3_4 = attributes\n",
    "        # 第一类的期望值μ\n",
    "    e_c1_1 = np.mean(c1_1)\n",
    "    e_c1_2 = np.mean(c1_2)\n",
    "    e_c1_3 = np.mean(c1_3)\n",
    "    e_c1_4 = np.mean(c1_4)\n",
    "        # 第二类的期望值μ\n",
    "    e_c2_1 = np.mean(c2_1)\n",
    "    e_c2_2 = np.mean(c2_2)\n",
    "    e_c2_3 = np.mean(c2_3)\n",
    "    e_c2_4 = np.mean(c2_4)\n",
    "        # 第三类的期望值μ\n",
    "    e_c3_1 = np.mean(c3_1)\n",
    "    e_c3_2 = np.mean(c3_2)\n",
    "    e_c3_3 = np.mean(c3_3)\n",
    "    e_c3_4 = np.mean(c3_4)\n",
    "    return [e_c1_1, e_c1_2, e_c1_3, e_c1_4,\n",
    "            e_c2_1, e_c2_2, e_c2_3, e_c2_4,\n",
    "            e_c3_1, e_c3_2, e_c3_3, e_c3_4]\n",
    "# 计算每一类的方差\n",
    "def cal_var(attributes):\n",
    "    c1_1, c1_2, c1_3, c1_4, c2_1, c2_2, c2_3, c2_4, c3_1, c3_2, c3_3, c3_4 = attributes\n",
    " \n",
    "    # 第一类的方差var\n",
    "    var_c1_1 = np.var(c1_1)\n",
    "    var_c1_2 = np.var(c1_2)\n",
    "    var_c1_3 = np.var(c1_3)\n",
    "    var_c1_4 = np.var(c1_4)\n",
    "    # 第二类的方差s\n",
    "    var_c2_1 = np.var(c2_1)\n",
    "    var_c2_2 = np.var(c2_2)\n",
    "    var_c2_3 = np.var(c2_3)\n",
    "    var_c2_4 = np.var(c2_4)\n",
    "    # 第三类的方差s\n",
    "    var_c3_1 = np.var(c3_1)\n",
    "    var_c3_2 = np.var(c3_2)\n",
    "    var_c3_3 = np.var(c3_3)\n",
    "    var_c3_4 = np.var(c3_4)\n",
    "    return [var_c1_1, var_c1_2, var_c1_3, var_c1_4,\n",
    "            var_c2_1, var_c2_2, var_c2_3, var_c2_4,\n",
    "            var_c3_1, var_c3_2, var_c3_3, var_c3_4]\n",
    "# 计算先验概率\n",
    "def cal_prior_probability(Y):\n",
    "    a = b = c = 0\n",
    "    for i in Y:\n",
    "        if (i == 0):\n",
    "            a += 1\n",
    "        elif (i == 1):\n",
    "            b += 1\n",
    "        elif (i == 2):\n",
    "            c += 1\n",
    "        else:\n",
    "            pass\n",
    "    pa = a / len(Y)\n",
    "    pb = b / len(Y)\n",
    "    pc = c / len(Y)\n",
    "    return pa, pb, pc\n",
    "\n",
    "def cal_posteriori_probability(X, Y, p, means, vars):\n",
    "    pa, pb, pc = p\n",
    "    e_c1_1, e_c1_2, e_c1_3, e_c1_4, e_c2_1, e_c2_2, e_c2_3, e_c2_4, e_c3_1, e_c3_2, e_c3_3, e_c3_4 = means\n",
    "    var_c1_1, var_c1_2, var_c1_3, var_c1_4, var_c2_1, var_c2_2, var_c2_3, var_c2_4, var_c3_1, var_c3_2, var_c3_3, var_c3_4 = vars\n",
    "    X1 = X[:, 0]\n",
    "    X2 = X[:, 1]\n",
    "    X3 = X[:, 2]\n",
    "    X4 = X[:, 3]\n",
    "    Y_validation_new = []\n",
    "    true_test = 0\n",
    "    false_test = 0\n",
    "    for i in range(len(X1)):\n",
    "        # 计算后验概率=P(X|Y=C1)P(Y=C1)\n",
    "        P_1 = stats.norm.pdf(X1[i], e_c1_1, var_c1_1) * stats.norm.pdf(X2[i], e_c1_2, var_c1_2) * stats.norm.pdf(\n",
    "            X3[i], e_c1_3,\n",
    "            var_c1_3) * stats.norm.pdf(\n",
    "            X4[i], e_c1_4, var_c1_4) * pa\n",
    "        # 计算后验概率=P(X|Y=C2)P(Y=C2)\n",
    "        P_2 = stats.norm.pdf(X1[i], e_c2_1, var_c2_1) * stats.norm.pdf(X2[i], e_c2_2, var_c2_2) * stats.norm.pdf(\n",
    "            X3[i], e_c2_3,\n",
    "            var_c2_3) * stats.norm.pdf(\n",
    "            X4[i], e_c2_4, var_c2_4) * pb\n",
    "        # 计算后验概率=P(X|Y=C3)P(Y=C3)\n",
    "        P_3 = stats.norm.pdf(X1[i], e_c3_1, var_c3_1) * stats.norm.pdf(X2[i], e_c3_2, var_c3_2) * stats.norm.pdf(\n",
    "            X3[i], e_c3_3,\n",
    "            var_c3_3) * stats.norm.pdf(\n",
    "            X4[i], e_c3_4, var_c3_4) * pc\n",
    "        # 计算判别函数，选取概率最大的类\n",
    "        max_P = max(P_1, P_2, P_3)\n",
    "        if (max_P == P_1):\n",
    "            Y_validation_new.append(0)\n",
    "            if (Y[i] == 0):\n",
    "                true_test += 1\n",
    "            else:\n",
    "                false_test += 1\n",
    "        elif (max_P == P_2):\n",
    "            Y_validation_new.append(1)\n",
    "            if (Y[i] == 1):\n",
    "                true_test += 1     \n",
    "            else:\n",
    "                false_test += 1\n",
    "        elif (max_P == P_3):\n",
    "            Y_validation_new.append(2)\n",
    "            if (Y[i] == 2):\n",
    "                true_test += 1\n",
    "            else:\n",
    "                false_test += 1\n",
    "        else:\n",
    "            false_test += 1\n",
    "    return Y_validation_new\n",
    "\n",
    "def paint_train(X_train, Y_train):            \n",
    "    x1 = X_train[Y_train == 0, 0]\n",
    "    y1 = X_train[Y_train == 0, 1]\n",
    "    z1 = X_train[Y_train == 0, 2]\n",
    "    x2 = X_train[Y_train == 1, 0]\n",
    "    y2 = X_train[Y_train == 1, 1]\n",
    "    z2 = X_train[Y_train == 1, 2]\n",
    "    x3 = X_train[Y_train == 2, 0]\n",
    "    y3 = X_train[Y_train == 2, 1]\n",
    "    z3 = X_train[Y_train == 2, 2]\n",
    "    ax = plt.subplot(111, projection='3d')\n",
    "    ax.scatter(x1, y1, z1, c = 'red')\n",
    "    ax.scatter(x2, y2, z2, c = 'blue')\n",
    "    ax.scatter(x3, y3, z3, c = 'green')\n",
    "    plt.show()\n",
    "    \n",
    "def paint_validation(X_validation, Y_validation):            \n",
    "    x1 = X_validation[Y_validation == 0, 0]\n",
    "    y1 = X_validation[Y_validation == 0, 1]\n",
    "    z1 = X_validation[Y_validation == 0, 2]\n",
    "    x2 = X_validation[Y_validation == 1, 0]\n",
    "    y2 = X_validation[Y_validation == 1, 1]\n",
    "    z2 = X_validation[Y_validation == 1, 2]\n",
    "    x3 = X_validation[Y_validation == 2, 0]\n",
    "    y3 = X_validation[Y_validation == 2, 1]\n",
    "    z3 = X_validation[Y_validation == 2, 2]\n",
    "    ax = plt.subplot(111, projection='3d')\n",
    "    ax.scatter(x1, y1, z1, c = 'red')\n",
    "    ax.scatter(x2, y2, z2, c = 'blue')\n",
    "    ax.scatter(x3, y3, z3, c = 'green')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制训练集三维图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "dataset = load_dataset()\n",
    "X_train, X_validation, Y_train, Y_validation = split_dataset(dataset)\n",
    "paint_train(X_train, Y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制测试集正确三维图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "attributes = split_out_attributes(X_train, Y_train)\n",
    "means = cal_mean(attributes)\n",
    "vars = cal_var(attributes)\n",
    "prior_p = cal_prior_probability(Y_train)\n",
    "Y_validation_new = cal_posteriori_probability(X_validation, Y_validation, prior_p, means, vars)\n",
    "paint_validation(X_validation, Y_validation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制测试集预测三维图像"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "Y1 = np.array(Y_validation_new)\n",
    "paint_validation(X_validation, Y1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "正态分布贝叶斯决策二维决策面部分展示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ P(\\omega_i|X) = \\frac{P(X|\\omega_i)P(\\omega_i)}{\\sum_{j=1}^M P(X|\\omega_j)P(\\omega_j)} = \\frac{P(X|\\omega_i)P(\\omega_i)}{P(X)} $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ p(x)=\\frac{1}{\\sqrt{2\\pi}\\sigma} exp[-\\frac{1}{2}(\\frac{x-\\mu}{\\sigma})^2] = N(\\mu,\\sigma^2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$ \\sigma^2 = E(x) = \\int_{-\\infty}^\\infty xp(x)dx$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#\n",
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "#\n",
    "classAData = [[0, 2, 1], [0, 1, 0]]\n",
    "classBData = [[-1, -2, -2], [1, 0, -1]]\n",
    "classA = np.array(classAData, dtype = np.float64)\n",
    "classB = np.array(classBData, dtype = np.float64)\n",
    "PirorclassA = 1/2\n",
    "PirorclassB = 1/2\n",
    "\n",
    "AMat = np.matrix(classA)\n",
    "ACovMat = np.matrix(np.cov(AMat))\n",
    "ACovDet = np.linalg.det(np.cov(AMat))\n",
    "ACovInv = ACovMat.I\n",
    "Amu = np.array([[1], [1/3]], dtype=np.float64)\n",
    "vA = -1/2 * ACovInv\n",
    "omegaA = ACovInv * Amu\n",
    "omegaA0 = -1/2 * np.matrix(Amu).T * ACovInv * Amu - 1/2 * math.log(abs(ACovDet)) + math.log(PirorclassA)\n",
    "\n",
    "BMat = np.matrix(classB)\n",
    "BCovMat = np.matrix(np.cov(BMat))\n",
    "BCovDet = np.linalg.det(np.cov(BMat))\n",
    "BCovInv = BCovMat.I\n",
    "Bmu = np.array([[-5/3], [0]], dtype=np.float64)\n",
    "vB = -1/2 * BCovInv\n",
    "omegaB = BCovInv * Bmu\n",
    "omegaB0 = -1/2 * np.matrix(Bmu).T * BCovInv * Amu - 1/2 * math.log(abs(BCovDet)) + math.log(PirorclassB)\n",
    "#\n",
    "AllCov = ACovMat + BCovMat\n",
    "AllCovInv = AllCov.I\n",
    "omegaAall = AllCovInv * Amu\n",
    "omegaA0all = -1/2 * np.matrix(Amu).T * AllCovInv * Amu + math.log(PirorclassA)\n",
    "omegaBall = AllCovInv * Bmu\n",
    "omegaB0all = -1/2 * np.matrix(Bmu).T * AllCovInv * Bmu + math.log(PirorclassB)\n",
    "omegaABall = omegaAall - omegaBall\n",
    "#\n",
    "x = np.arange(-10.1, 10.1, .01)\n",
    "y = np.arange(-10.1, 10.1, .01)\n",
    "x, y = np.meshgrid(x, y)\n",
    "x1Mean = [0, 0]\n",
    "x2Mean = [2/3, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = omegaABall[0, 0]*x + omegaABall[1, 0]*y + (omegaA0all-omegaB0all)\n",
    "plt.figure()\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.title('Every class covs is equal')\n",
    "plt.contour(x, y, f, 0, colors='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y5aX/geqd/E5lwrBCY4yJPfuWwvxr4dA6aPkL6PCknXwZYIlVaI7ugOyjkFLe7yTGmHORmwPrnoaVj0LZWtBvCtQd5HcqU4TAjoUtIttEZJWILBeR9DDLRUReFJHNIrJSRIreZz6+ByZ1gq/PeDhjTNAd3gbT+8GKB905McNXWZGJEYEtNJ5+qtpBVcONejcMaOFdRgOvFvlolVq6QfWmdIc1f3DfjowxwaYKW9+GCe1g/3LXo6znh1Cmut/JTDEFvdAUZgTwd3UWAFVFpPCJvUtVguEroeH3YcVDML2v+5ZkjAmmk/th3kj4/Dqo1t79/zb9iZ0bE2OCXGgUmCIiS0RkdJjl9YEdIb9neLedRkRGi0i6iKRnZWVB6WrQ833o/jYcWOm+JW19231rMsYER+ZM9/+542PXbXnALJteOUYFudD0VNVOuCay20WkT77l4b7SnFEtVHWsqqapalpqaqp3T4Gm18KwFe5b0ufXwbxr3LcnY4y/ck7Asvtg+gBIqQCDP/cmJrNzY2JVYAuNqu70fu4BxgFd862SATQM+b0BsPOsnqRiE/ctqd0TsONfMKE9ZM4+58zGmPN0cB1M6QbrnoELRsPQJTYxWRwIZKERkQoiUinvOjAYWJ1vtfHAdV7vs27AQVXdddZPlpQMbR+CwfMhuazr1bL8124OC2NMdKjCplddr9CjGdDn39D1NbdHY2JeUM+jqQ2ME3fALwV4T1UnicitAKr6GjABGA5sBo4CN5zXM9boAkOXwtK7YO2TsHsa9HgXKrc8r4c1xhTheBYsvAm++g/UHQLd3oRyhffrMbFFNIEOgqelpWl6ejHOodnxMSy8GXJPQucXodkN1svFmEjYNQU+HwUn90GHp6DVL0AC2dCS0ERkSQGnmRSLvaLhNPye60ZZo6v7pjX3ausoYExJyjkBS38FM4e482GGLIYL77IiE6fsVS1I+QbQf5obQynjE9dRYM8cv1MZE/sOrncH/Nc/By1ugyHpUK2d36lMBFmhKYwkQev7XffKpDLe8BePQG6238mMiT2qsPkv3gH/HdBnPHQZY4NhJgArNMVRIw2GLYOm18GaJ2BaHxtRwJizcXK/a4JedIubmGzYSmhwud+pTJRYoSmuUhVdb5ge78PBNTCxA2z/yO9UxgTfnrkwoYNrgu7wFPSfAuXr+Z3KRJEVmrPVZCQMW+4mWpr3Q9c7LfuI36mMCZ7cHFj1GEy/FJJS3Llqre+zA/4JyF7xc1GxKQyaA61/DV+8AZPSYP9Kv1MZExxHM2DGAFj1G2h8jWt6rtHF71TGJ1ZozlVSKejwB+g/FU4egMldYeMrNjinMV996pqW96VDt79Bj3egVGW/UxkfWaE5X3UGwPAVULs/pN8Oc6+yc25MYso5AUvuhtmXQ/mGbqSNZqP8TmUCwApNSShbC/p+Ch2fgYzxMLEj7F3gdypjouebL2BqT9jwJ2j5cxi8wIZvMv9jhaakSBJcdA8MmgcITO0Na58BzfU7mTGRtf0j9+Xq8BboPQ7SXoTkMn6nMgFihaak1ezqDnw2GAHL73PNCMf3+p3KmJKXcxwW/cz1vqza1r3vG37X71QmgKzQRELpqtDrH5D2shsFelJHyJrndypjSs6hTTC5G2x+DS66FwbOhgqN/U5lAsoKTaSIQMvbvx2+ZtqlsPZpa0ozsW/7h98OI3Ppp9DxadcL05gCWKGJtOqd3CyBDa6E5ffD7BFwYp/fqYw5ezknYPHtMG8kVL3Ynbhc/zt+pzIxwApNNJSuAr0+gs4vwe7J7tvg14v9TmVM8R3e6nqVbXoFLvyV11TWsOj7GYMVmugRgVZ3eL3ScP+0G8fYCZ4m+L76FCZ2gm82Q59PoNP/WVOZOStWaKItb8roOoMg/Q6Yfy2cOux3KmPOlJsDyx90PScrNoVhS11vSmPOUuAKjYg0FJGZIrJORNaIyJ1h1ukrIgdFZLl3edSPrOesTHW49D/Q7gn48gOYcgkc2uB3KmO+dXwPzBwMa/8IzW92A2JWbOZ3KhOjUvwOEEY28CtVXSoilYAlIjJVVdfmW+8zVb3Mh3wlQ5Kg7UNQ8xKYdw1M6gLd/+amkTbGT3sXuqGUTuyFS96A5jf4ncjEuMDt0ajqLlVd6l3/BlgH1Pc3VQTVGeia0qpcBJ99H5b/2jVZGBNtqrDpzzCtN0gpGDTfiowpEYErNKFEpAnQEVgYZnF3EVkhIhNFpE0hjzFaRNJFJD0rKytCSc9ThYYwcA5c8FNY+yTMGgYnvvY7lUkkOcfd7JeLb4XaA2BoOlTv6HcqEycCW2hEpCLwL+AuVT2Ub/FSoLGqtgdeAj4p6HFUdayqpqlqWmpqauQCn6/kMtD1NbjkL7BntjfHzXK/U5lEcDTDnVD8xV+hzUPuJMwy1f1OZeJIIAuNiJTCFZl3VfXj/MtV9ZCqHvauTwBKiUjNKMeMjOY3wcDPIPcUTOnhzsI2JlKy5rkvNQfXQu+Pof0TkJTsdyoTZwJXaEREgL8C61T1uQLWqeOth4h0xf0d8dPWVLOr13TR2Z2FbcdtTCRsfh2m94OUSjBkITS80u9EJk4FsddZT+AnwCoRyWs7ehBoBKCqrwFXAT8TkWzgGDBSNc7OfCxXB/pPhyU/d8dtDqyGnu/aTIXm/OWechOUbRoDdYdAz/ehdDW/U5k4JvH2+VyYtLQ0TU9P9zvG2dv4Ciz5BVRu5c6/sfMZzLk6sQ/mXg2Z091QMh2esqYyUyQRWaKqaed6/8A1nZkwWt4G/abAsV0wuSvsmeN3IhOLDm2EKd0g6zPo9qY3lIwVGRN5VmhiRZ3+MHghlKkJMwbClrf8TmRiSeZMV2RO7ndNss2u9zuRSSBWaGJJ5RZufpvU3rDgeljxiA3KaYq25W8wYzCUrQNDFkGtXn4nMgnGCk2sKV0N+k1y3aDXPOEG5cw54XcqE0SqsPJRWHAD1O7rjVfW1O9UJgEFsdeZKUpSKej6OlRsDisehGM7oc84N4W0MeB6li28Gbb+HZrd6E4GtqH9jU9sjyZWiUCbX0P3d2DvPJja253hbcypb2DWZa7IXPw7N9qEFRnjIys0sa7pj6HvRDiy3Y0kcHCd34mMn45nuZMwM6fDJX+Fix91X0qM8ZEVmnhQZ4CbWjf3pBt516aJTkxHtsPUXm44mT6fQPMb/U5kDGCFJn5U7+imiU6pDNP7Q+YsvxOZaDq0wRWZ45nQfyrUj92pmkz8sUITTyo1h0FzoUIjN9XAzol+JzLRsH8lTOvj9mgHzobUnn4nMuY0VmjiTfl6MGA2VL4I5oyAjPF+JzKRtG+ZOyYjpdycRtXa+53ImDNYoYlHZWvCgBlQraObtTPj334nMpGwbynMGAApFWHQHDcWnjEBZIUmXpWu6sZHq94Z5v4AvvrU70SmJO1f4YYiKlXZNZfZQKsmwKzQxLPSVaDfZKjaHj67CnZP9zuRKQkH18OMQZBSAQbMhIpN/E5kTKGs0MS7vGJTuaU7ZrN3od+JzPk4st3tyUiSGxzThpQxMcAKTSIoU901o5WtA7OGu2/EJvac+BpmDoHsw+71rNzS70TGFIsVmkRRro7bs0lKcV2fj2X6ncicjZzjbo/08DY3+V21dn4nMqbYrNAkkkrN4dJP3Ul9c0a4Dy8TfKqw4EbImgc93oZavf1OZMxZKbTQiEhlEWke5vaIf50SkaEiskFENovIA2GWlxGRD73lC0WkSaQzxYUaXaDHu/D1Qlg42uaziQVrn4Tt70P7P0CjH/idxpizVmChEZGrgfXAv0RkjYh0CVn8t0iGEpFkYAwwDGgNXCMirfOtdhOwX1UvAJ4HnopkprjS8Eo3qu+2t2HjGL/TmMLsmgIrHoLGI6H1Gd+3jIkJhe3RPAh0VtUOwA3A2yLyPW9ZpIeD7QpsVtUtqnoS+AAYkW+dEUDefMb/BAaI2DC1xdb2Yah3GSz7pQ3CGVRHd8L8H0OVNm6of3t7mxhVWKFJVtVdAKq6COgHPCQivwAi3d5SH9gR8nuGd1vYdVQ1GzgI1Mj/QCIyWkTSRSQ9KysrQnFjkCRB97dcT7R518Cpw34nMqE0Fz6/DrKPQq9/uHNmjIlRhRWab0KPz3hFpy9uT6JNhHOF++qWv7gVZx1UdayqpqlqWmpqaomEixtlqkOPd+DwFlh2r99pTKiNY9ycMp3/BFUu9DuNMeelsELzMyAp9NiIqn4DDAVujnCuDKBhyO8NgJ0FrSMiKUAVYF+Ec8WfWn3gwrth82uwZ47faQy4kzKXPwB1h0HzSP+rGRN5BRYaVV2hqpuAj0TkfnHKAc8Bt0U412KghYg0FZHSwEgg/zDE44FR3vWrgBmq1oXqnLR7HCo0gcU/c3PNG38tudP97PqaHZcxcaE459FcgttzmI8rADuBiE544R1zuQOYDKwDPlLVNSLymIhc4a32V6CGiGwGfglYl5xzlVLeNdEcXAub/ux3msS2e4YbbbvtI25eIWPiQEox1jkFHAPKAWWBraqaG9FUgKpOACbku+3RkOvHATupoKTUvwJqXQprHndTAKeU9ztR4lGFFb+G8g3hwrv8TmNMiSnOHs1iXKHpAvTCndPyz4imMtEnAu2egON7YPPrfqdJTLunwteL3N5Mclm/0xhTYopTaG5S1UdV9ZSq7lbVEYDNpBWPavWC1F6w4QXIzfE7TeJZ/zyUqwtNr/M7iTElqshCo6rpYW57OzJxjO9a3gFHtrqutSZ6jmyHXZOh+WhILuN3GmNKlA2qaU7X4LtQqgpse8/vJIll+4eAQrNRRa5qTKyxQmNOl1wG6l8OOz91Z6eb6PhqPFTrZBOZmbhkhcacqe5gN8nWgVV+J0kM2UfczKd1h/idxJiIsEJjzlSzu/tpg21Gx/4VoNnfbndj4owVGnOmis0guRwcWud3ksSQt52rRnoIQWP8YYXGnEmSoHwDOJrhd5LEkLedyzcsfD1jYpQVGhNeqapw6qDfKRLDyYOQUhGSSvmdxJiIsEJjwpNk63UWNbluL9KYOGXvbhNezhEb7yxaksu7Cc5s8HETp6zQmPCO7XKzb5rIK1vb9To7sdfvJMZEhBUac6YTX7sPvUoX+J0kMeRt50Mb/M1hTIRYoTFn+tob3q5aB39zJIpqHd3PfWcMK2hMXLBCY860ZyZICtTo5neSxFC+njt3KXOG30mMiQgrNOZ0qm6Gx1p9oFRFv9MkjrrDYPc0NxyNMXHGCo053f6lcGg9NLLJS6Oq8dWQcwx2jPM7iTElLlCFRkSeEZH1IrJSRMaJSNUC1tsmIqtEZLmIWMN2Sdr0mht+pvFIv5MkltReULE5bH7N7yTGlLhAFRpgKtBWVdsBG4FfF7JuP1XtoKpp0YmWAI7thq1vQ9OfQOmwNd5EiiS5Seey5sHeBX6nMaZEBarQqOoUVc32fl0ANPAzT8JZ+zToKbjwHr+TJKbmN0OZGrDqt34nMaZEBarQ5HMjMLGAZQpMEZElIjK6sAcRkdEiki4i6VlZWSUeMm4c3gqbxkDTUVC5hd9pElOpitD6ATel826bStvEj6gXGhGZJiKrw1xGhKzzEJANvFvAw/RU1U7AMOB2EelT0POp6lhVTVPVtNTU1BL9W+LK0rtdl+Z2j/udJLG1vAMqNIUld0LuKb/TGFMiUqL9hKo6sLDlIjIKuAwYoBp+8CdV3en93CMi44CuwJySzpowdnziujR3eBLK1/c7TWJLLgudX4A5V8C6Z6DNg34nMua8BarpTESGAvcDV6jq0QLWqSAilfKuA4OB1dFLGWeO74XFt0LV9nDhL/1OYwAaXA4Nr4JVv4MD9tY2sS9QhQZ4GagETPW6Lr8GICL1RGSCt05tYK6IrAAWAf9V1Un+xI1xqrDoFji5D7q/ZfOhBEmXMa7n3/wfQ85xv9MYc16i3nRWGFUNO4qj11Q23Lu+BWgfzVxxa+PLkPEJdHwWqtkmDZSyteCSN2H2d2DJ3dD1Vb8TGXPOgrZHY6Ilaz4s+xXUvxwuvMvvNCac+sPhonvdSZxb3/Y7jTHnzApNIjqaAZ99H8o3ck1mNrtjcLX/A9TqCwtvga8X+53GmHNinzCJ5tRhmH2FG7yxz7+hdDW/E5nCJKVAr4+gXF1uyGnfAAAUAElEQVT3uh3Z4XciY86aFZpEknsK5v0QDqyAXh9C1TZ+JzLFUTYVLv0Uco7CrOFw8oDfiYw5K1ZoEoUqLPop7JwAXV6FesP8TmTORtU20Ptj+GYDzBkB2cf8TmRMsVmhSQSqsOwe2PImtP0NXFDoqD0mqOoMgG5/hz2fuT1TGznAxAgrNIlg1e9g/XNueJOLf+N3GnM+moyEtJfhq//A59dBbo7fiYwpUqDOozERsPr3sPp30OwGN7SJiN+JzPlqeRtkH4bl94OUgm5vQlKy36mMKZAVmni2+vew8mFoci10fd26MceT1vdB7klY+Yj73YqNCTArNPFI1c1psvoxaPIT+xCKV20fdj9XPgKabcMImcCyQhNvVGHZvbD+WWh2I3Qda0UmnrV9GJJKu2a0nGPQ8wNILuN3KmNOY20p8SQ3x3VhXv+sO/B/yetWZBJB6/ug80tu3LrZl7mTco0JECs08SLnhOvy+sXr0OYh6PyiHZNJJK3ugG5/g8wZMGOAm/7BmICwT6J4cPIgzBoGO/4FnZ6D9k9Y77JE1GyUO6lz/wqY1guObPc7kTGAFZrYd/QrmNbHncTX/R248G6/Exk/NRgB/afCsUyY0h32L/c7kTFWaGLagdXuw+TwFug7AZr+2O9EJghq9YZBn4Ekw9Q+sGuK34lMgrNCE6t2TYWpPUFz3IdK3UF+JzJBUrUtDF4AFZu6gTg3/8XvRCaBWaGJRZtfd8dkKjR2HybVOvidyARR+fruS0idgW7K7uUPgOb6ncokoMAVGhH5rYh8JSLLvcvwAtYbKiIbRGSziDwQ7Zy+yM2BpffAotFQZxAMmgsVGvqdygRZqcpuioELboW1T8HcH7i5iIyJosAVGs/zqtrBu0zIv1BEkoExwDCgNXCNiLSOdsioOvUNzPnut+fIXPof9yFiTFGSUqDLK65HYsYnMLW3m2XVmCgJaqEpSldgs6puUdWTwAfACJ8zRc7hLe6g/66JkDYG0l5yHx7GFJeI65HYZzx8sxkmdYG9C/xOZRJEUAvNHSKyUkTeEJFwcw3XB0LntM3wbjuDiIwWkXQRSc/KyopE1sjKnAmTu8KxndBvkhu515hzVf87MPhzSCkP0y6FLW/5ncgkAF8KjYhME5HVYS4jgFeB5kAHYBfwbLiHCHObhnsuVR2rqmmqmpaamlpif0PEqcKGl2HGIChTC4Yscgd1jTlfVdu491NqL1hwPSz5JeRm+53KxDFf2l9UtVifmCLyOvBpmEUZQOhR8AbAzhKIFgw5x2HxbW5GzPpXQI+37XiMKVllarg95KX3wIbn4cBKNyBn2Zp+JzNxKHBNZyJSN+TXK4HVYVZbDLQQkaYiUhoYCYyPRr6IO7LDnWS35U1o+yj0GWdFxkRGUilIe8FNI5E1Fyanwb5lfqcycShwhQZ4WkRWichKoB9wN4CI1BORCQCqmg3cAUwG1gEfqeoavwKXmMxZMKkzHFoPvcdBu9/ZwJgm8ppd78630RyY2gO2vu13IhNnRDXsoY24lJaWpunp6X7HOJMqrH/OzSlSqYUrMlUu9DuVSTTH98Dcq2HPbNeFvuOzkFza71QmAERkiaqmnev97euy305944b3X3aPGxBxyCIrMsYfZWtB/2lw4S9h48swva8btNWY82SFxk8H18LkLm54/w5PQ69/QqlKfqcyiSwpBTo9Cz0/dB0EJnaE3TP8TmVinBUav2x7z50fc3I/9J8Ore+1OWRMcDS+GoYshjI1YeYgWPNHGyfNnDMrNNGWc8J1XZ7/Y6jWEYYug9p9/U5lzJmqXOSachtdDSsehNlXwIl9fqcyMcgKTTQd3uqG9t/0Klx0DwyYAeXr+Z3KmIKVqgg93oO0l2H3FJjUCfYu8juViTFWaKIl498wsZMbZ6rPJ9DxGXcegzFBJwItb4eBc93v03rBhhddb0ljisEKTaTlnHRDfMz5LlRqDsOWut5lxsSaml1h6FKoOxSW3Alzr4KTB/xOZWKAFZpIOrwNpvVxQ3y0vAMGzYOKzfxOZcy5K1Md+vzb7ZFnjHd76V8H8Nw0EyhWaCJlxyeua+ihddDrH25o/+Qyfqcy5vyJuGOMA+eAZrvRBNa/YE1ppkBWaEpazglIvxM+uxIqXQDDlkGjq/xOZUzJS+0Ow5a7prSld7n3vPVKM2FYoSlJhzbBlB6w8UVodaebatmaykw8y2tK6/Qc7JwAEztA1ny/U5mAsUJTUra+67p+Htnm/vE6/8maykxiyJu9c9A815NyWh87wdOcxgrN+Tp1GBbcAJ9fC9U6uKaEBlf4ncqY6KvRxfVKa3iVO8FzxmA4tsvvVCYArNCcj33L3LD+W96Cto/AgJlQoWHR9zMmXpWuAj3fh66vw975MKE97JzodyrjMys050LV9bKZ0g2yD7sz/Ns95gYkNCbRicAFN8PQdChXB2YNh6W/ch1lTEKyQnO2jmfB7MtdL5u6Q2DYChurzJhwqrSGwQuhxW1uvqUpPeDQRr9TGR9YoTkbu6bChHawexp0ftEd9Lc51o0pWEo56DLGDbt0ZJvrMPPFm3bOTYKxQlMcOSdh2X0wczCUruZGtG31cxvW35jiajAChq+E6l1g4Y0w7xobviaBBOqggoh8CLTyfq0KHFDVDmHW2wZ8A+QA2eczxWiRDm10/xT7l8IFP3XnC6SUj9jTGRO3ytd3M3iuewpWPgp7P4ce70KtXn4nMxEWqEKjqj/Muy4izwIHC1m9n6rujWAY2PIGpP8CkstC73HQ8LsRezpjEkJSMrR5EGoPgPk/gumXQpuHXa9N60wTtwLZdCYiAlwNvO9LgBP7YO4PYOHNULOb2+W3ImNMyal5iTvnrMm1sPoxd5Ln4S1+pzIREshCA/QGMlV1UwHLFZgiIktEZHRhDyQio0UkXUTSs7Kyin7mzJnugP9X46HDU9B/qtvlN8aUrFKVoPtb0ON9OLgWJnSArW9bR4E4FPVCIyLTRGR1mEvoJC3XUPjeTE9V7QQMA24XkT4FraiqY1U1TVXTUlNTC37EnJOw7H6YPgBSKsDgz6H1fSBBrcXGxIkmI2H4CqjWHj6/zjWpWUeBuBL1RlFVHVjYchFJAb4HdC7kMXZ6P/eIyDigKzDnnEMdXO/e3PuXwQWjvQP+Fc754YwxZ6lCYxgwC9b+EVb91g3M2eNtqFXgd0gTQ4L4dX0gsF5VM8ItFJEKIlIp7zowGFh9Ts+kCptedX37j+5wff27/tmKjDF+SEqGtg/DoPmQVBqm9YXlD7rWBhPTglhoRpKv2UxE6onIBO/X2sBcEVkBLAL+q6qTzvpZjmW6M/wX3+a+NQ1faVMsGxMENbu6eZya3+j2cKb2cK0OJmaJJtCBt7S0NE1PT4evPoUFN8KpQ9DxaTfNsh2LMSZ4doyDRbdA9lHo9CxccKudKO0DEVlyPucrJtanq+bColvdnky5ejB0CbT6hRUZY4Kq4ZUwfBWk9natD7Mvd60RJqYk1ifsobWweayb73zIQqjaxu9ExpiilKsL/SZC5xfcOIMTLoaM8X6nMmchsQqN5sKA6dDxGZv90phYIkmu9WHYUnde25wRsHC0m3jQBF5iFZoqbaF2P79TGGPOVd7UA63vhy/+AhM7wN4FfqcyRUisQmPHYoyJfcmlocOTMHAWaDZM7ekG6cw95XcyUwD75DXGxKZafdzEg02uhdWPexOrbfA7lQnDCo0xJnaVruLGS+v1Tzco58SOsHGMjZcWMFZojDGxr9H34TurodalkH4HzBwKR7/yO5XxWKExxsSHcnWh7wTo8gpkzXXdoLd/6HcqgxUaY0w8EYEWP3ND2FRqCfNGwrwfwcn9fidLaFZojDHxp3JLGDQXLn4MvvwH/Pdi2DXV71QJywqNMSY+JaXAxY/AkAVQqjLMHAzpP3fjppmoskJjjIlv1Tt74xreCRtfdj3T9i7yO1VCsUJjjIl/KeWg85+g/3TIOeamHrCTPKPGCo0xJnHU6e9Gg27yY3eS5+RucGCN36ninhUaY0xiyTvJs/fHcPRLmNQZ1j3rBt01EWGFxhiTmBpeCcNXQ72hsOwemN4PDm/1O1VcskJjjElc5WpD73HQ7U3YvxwmtIPNf7EhbEqYL4VGRH4gImtEJFdE0vIt+7WIbBaRDSIypID7NxWRhSKySUQ+FJHS0UlujIk7ItDsehi+Emp0dVNHz74Mju3yO1nc8GuPZjXwPWBO6I0i0hoYCbQBhgKviEhymPs/BTyvqi2A/cBNkY1rjIl7FRpD/6luJs/MGfDftjaETQnxpdCo6jpVDTee9wjgA1U9oapbgc1A19AVRESA/sA/vZveAr4bybzGmATxv5k8l0OlFm4Im7k/hBNf+50spgXtGE19YEfI7xnebaFqAAdUNbuQdf5HREaLSLqIpGdlZZVoWGNMnKrcyg1h0+4JyBgHm//sd6KYlhKpBxaRaUCdMIseUtV/F3S3MLflPypXnHW+XaA6FhjrZcoSkSPA3oLWD5CaBD9nLGSE2MgZCxkhNnJGIOND3qVExdK2bHw+DxKxQqOqA8/hbhlAw5DfGwA7862zF6gqIineXk24dQrKlCoi6aqaVvTa/oqFnLGQEWIjZyxkhNjIGQsZITZyllTGoDWdjQdGikgZEWkKtABOG5RIVRWYCVzl3TQKKGgPyRhjjM/86t58pYhkAN2B/4rIZABVXQN8BKwFJgG3q2qOd58JIlLPe4j7gV+KyGbcMZu/RvtvMMYYUzwRazorjKqOA8YVsOz3wO/D3D485PoW8vVGOwtjz/F+0RYLOWMhI8RGzljICLGRMxYyQmzkLJGMonYGrDHGmAgK2jEaY4wxccYKjTHGmIiKy0ITi2Opec+z3LtsE5HlBay3TURWeeulRzpXvuf+rYh8FZJzeAHrDfW272YReSCaGb3nf0ZE1ovIShEZJyJVC1gv6tuyqG3j9bj80Fu+UESaRCNXyPM3FJGZIrLO+x+6M8w6fUXkYMj74NFoZgzJUejrJ86L3rZcKSKdopyvVcg2Wi4ih0Tkrnzr+LItReQNEdkjIqtDbqsuIlO9z72pIlKtgPuO8tbZJCKjivWEqhp3F+AioBUwC0gLub01sAIoAzQFvgCSw9z/I2Ckd/014GdRzv8s8GgBy7YBNX3arr8F7ilinWRvuzYDSnvbu3WUcw4GUrzrTwFPBWFbFmfbALcBr3nXRwIfRnnb1QU6edcrARvDZOwLfBrNXOfy+gHDgYm4k7y7AQt9zJoM7AYaB2FbAn2ATsDqkNueBh7wrj8Q7v8GqA5s8X5W865XK+r54nKPRmN4LDXv+a8G3o/Wc5awrsBmVd2iqieBD3DbPWpUdYp+O0TRAtxJvUFQnG0zAveeA/ceHOC9J6JCVXep6lLv+jfAOgoZ4ingRgB/V2cB7kTvuj5lGQB8oarbfXr+06jqHGBfvptD33sFfe4NAaaq6j5V3Q9MxQ2AXKi4LDSFKPGx1CKgN5CpqpsKWK7AFBFZIiKjo5grzx1eM8QbBexaF2cbR9ONuG+14UR7WxZn2/xvHe89eBD3now6r9muI7AwzOLuIrJCRCaKSJuoBvtWUa9fkN6LIyn4y2MQtiVAbVXdBe4LB1ArzDrntE19OY+mJEhAxlI7G8XMfA2F7830VNWdIlILmCoi671vJyWisIzAq8DjuO3xOK6J78b8DxHmviXeh74421JEHgKygXcLeJiIbsswfH3/nQ0RqQj8C7hLVQ/lW7wU1wR02DtO9wluFI9oK+r1C8q2LA1cAfw6zOKgbMviOqdtGrOFRgM4llpRisosIim4eXo6F/IYO72fe0RkHK45psQ+HIu7XUXkdeDTMIuKs43PWzG25SjgMmCAeo3LYR4jotsyjOJsm7x1Mrz3QxXObOKIKBEphSsy76rqx/mXhxYeVZ0gIq+ISE1VjeoAkcV4/aLyXiyGYcBSVc3MvyAo29KTKSJ1VXWX18S4J8w6GbjjSnka4I6FFyrRms6CPpbaQGC9qmaEWygiFUSkUt513EHv1eHWjYR87dtXFvDci4EW4nrulcY1GYyPRr48IjIUN0zRFap6tIB1/NiWxdk243HvOXDvwRkFFcpI8I4H/RVYp6rPFbBOnbzjRiLSFfc5EtUJW4r5+o0HrvN6n3UDDuY1DUVZga0UQdiWIULfewV97k0GBotINa/pfLB3W+Gi3dshGhfch2AGcALIBCaHLHsI1/NnAzAs5PYJQD3vejNcAdoM/AMoE6XcfwNuzXdbPWBCSK4V3mUNrpkomtv1bWAVsNJ7U9bNn9H7fTiut9IX0c7oPf9mXDvycu/yWv6cfm3LcNsGeAxXFAHKeu+5zd57sFmUt10vXFPIypDtNxy4Ne+9CdzhbbMVuM4WPXx4jcO+fvlyCjDG29arCOmBGsWc5XGFo0rIbb5vS1zh2wWc8j4rb8IdC5wObPJ+VvfWTQP+EnLfG73352bghuI8nw1BY4wxJqISrenMGGNMlFmhMcYYE1FWaIwxxkSUFRpjjDERZYXGGGNMRFmhMSYARGSSiBwQkXAnwRoT06zQGBMMzwA/8TuEMZFghcaYKBKRLt6gpGW9s9vXiEhbVZ0OfON3PmMiIWbHOjMmFqnqYhEZDzwBlAPeUdWoDSNkjB+s0BgTfY/hxj07DvzC5yzGRJw1nRkTfdWBirgZLMv6nMWYiLNCY0z0jQUewc2T85TPWYyJOGs6MyaKROQ6IFtV3xORZGC+iPQHfgdcCFQUkQzgJlUtevh1Y2KAjd5sjDEmoqzpzBhjTERZoTHGGBNRVmiMMcZElBUaY4wxEWWFxhhjTERZoTHGGBNRVmiMMcZE1P8DaBZ3HM1jk7IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vAB = vA - vB\n",
    "omegaAB = omegaA - omegaB\n",
    "g = (vAB[0, 0])*(x**2) + (vAB[1, 1])*(y**2) + (vAB[0, 1] + vAB[1, 0])*(x*y) + omegaAB[0, 0]*x + omegaAB[1, 0]*y + (omegaA0-omegaB0)\n",
    "plt.figure()\n",
    "plt.xlabel('x1')\n",
    "plt.ylabel('x2')\n",
    "plt.title('Every class covs is not equal')\n",
    "plt.contour(x, y, g, 0, colors='orange')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
